A characterization of compact parts of \(L^ p\) spaces application to Sobolev embeddings. (Q595825)
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scientific article; zbMATH DE number 2084002
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of compact parts of \(L^ p\) spaces application to Sobolev embeddings. |
scientific article; zbMATH DE number 2084002 |
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A characterization of compact parts of \(L^ p\) spaces application to Sobolev embeddings. (English)
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6 August 2004
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This paper is divided into two parts. Firstly, the author develops a characterization of compact subsets of \(L^p(\Omega)\). More precisely, for a metric locally compact space \(\Omega\), the author defines a notion of equi-integrability which allows to state an Ascoli theorem for \(L^p(\Omega)\). In the second part, he develops a methodology to retrieve and improve standard results about Sobolev embeddings and compact embeddings \(W^{1,p}(\Omega)\to L^q(\Omega)\).
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compact subset of \(L^p(\Omega)\)
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Ascoli theorem for \(L^p(\Omega)\)
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embedding
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